Precision is the accuracy used to compute numbers (see the Precision fieldPrecision_field of the Options > Mode Settings > Simplification command19_L5FP).  A related but separate issue is the notation used to display numbers.


Numbers can be displayed using rational notation:  Integers are displayed as integers and fractions are displayed as ratios of integers.  Rational notation has the advantage that all stored numbers can be displayed exactly.  However, numbers that require many digits to display in rational notation are difficult to comprehend.


Thus, it is also possible to display fractions using decimal point notation.  It is also possible to display large magnitude and small magnitude numbers using scientific notation.  Finally, it is possible to display numbers in mixed notation using whichever style is most concise:  rational notation if a number is simple, decimal point notation if a number's magnitude is not extreme.  Otherwise use scientific notation.


You can also control the maximum number of fractional digits displayed in decimal point notation or the maximum number of significant digits displayed in scientific notation.  This number can be more, less, or the same as the number of digits of precision set in the Precision fieldPrecision_field of the Options > Mode Settings > Simplification command19_L5FP.  For decimal fraction, scientific, or mixed notation, it is usually advisable to display no more digits than are accurate and necessary for your purposes.  This policy avoids misleading results and increases comprehension.


Use the Notation and Digits fields of the Options > Mode Settings > Output command3L4YH to see and/or change the notation style and the number of digits used when displaying numbers on the screen and when saving numbers in mth files.  Regardless of the number in the Digits field, rational notation uses as many digits as necessary to display results.  Thus, set the Digits field to the digits you want displayed for decimal fraction, scientific, or mixed notation.


When a new notation style is selected, this command generates an expression of the form

Notation := style

where style is Decimal, Mixed, Rational, or Scientific.  When a new number of digits to display is entered, the command generates an expression of the form

NotationDigits := digits

where digits is a positive integer.  The notation style and digits to display can also be changed by entering on the expression entry line expressions of the above form using upper and lower case exactly as shown.


If you use the Precision fieldPrecision_field of the Options > Mode Settings > Simplification command19_L5FP to change the precision to exact mode, the notation style is automatically changed to rational.  If you change the precision to approximate mode, the notation style is changed to scientific.  If you change the precision to mixed mode, the notation style is changed to mixed.


If you use the Precision fieldPrecision_field of the Options > Mode Settings > Simplification command19_L5FP to change the number of digits of precision, the number of digits displayed is changed to the requested precision.


Normally these automatic changes made to the notation by the precision commands make it unnecessary for you to have to change the notation yourself.  However, if you want some other notation, the notation command must be issued after the precision command.


For example, if you use the Precision fieldPrecision_field of the Options > Mode Settings > Simplification command19_L5FP to set precision to approximate mode using 6 significant digits, then π simplifies to 3.14159, a decimal approximation for π.  Then if you use the Notation field of the Options > Mode Settings > Output command3L4YH to set the notation style to rational, then π simplifies to 355/113, a rational approximation for π.

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